Sales prediction with Auto Regressive Model.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Monthly Sales prediction of several items with Auto Regressive Model"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Load data\n",
    "\n",
    "- Training data (salesdata1.txt): contains sales data for 5 items (i=1...5) over 24 months (t=1...24)\n",
    "- Testing data (salestestdata.txt) : contain sales data for 5 items for months 25, 26,...,30."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "salesdata = textread('salesdata1.txt');\n",
    "salestestdata = textread('salestestdata.txt');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    }
   ],
   "source": [
    "NumOfMonths = size(salesdata,2);\n",
    "NumOfItems = size(salesdata,1);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
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FcY2Qa/GMQJh3TghsZF/g4u0qOskU6HvyySdvuOGGoUOH6rgcZVAiVT7NOEGl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\nEgAASAEBCQAApICABAAAUvg/rbtxH7E1gqwAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "figure();\n",
    "\n",
    "col = {'b-o','g-o','r-o','c-o','m-o'};\n",
    "\n",
    "% plot of salesdata\n",
    "for i = 1:NumOfItems\n",
    "    plot(salesdata(i,:),col{i});\n",
    "    hold on\n",
    "end\n",
    "\n",
    "hleg = legend('Item 1','Item 2','Item 3','Item 4','Item 5');\n",
    "set(hleg,'Location','northwest');\n",
    "xlabel('Month'), ylabel('Number of Items Sold'), title('Sales data')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Autoregressive (AR) Model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "A(:,:,1) =\n",
      "\n",
      "  Columns 1 through 11\n",
      "\n",
      "         388         371         371         399         412         506         488         498         521         502         884\n",
      "         386         388         371         371         399         515         506         488         498         521         942\n",
      "         360         386         388         371         371         476         515         506         488         498         947\n",
      "         365         360         386         388         371         463         476         515         506         488         937\n",
      "         381         365         360         386         388         482         463         476         515         506         946\n",
      "         376         381         365         360         386         499         482         463         476         515         994\n",
      "         350         376         381         365         360         479         499         482         463         476         989\n",
      "         354         350         376         381         365         486         479         499         482         463         970\n",
      "         379         354         350         376         381         538         486         479         499         482         997\n",
      "         375         379         354         350         376         567         538         486         479         499        1040\n",
      "         361         375         379         354         350         559         567         538         486         479        1062\n",
      "         370         361         375         379         354         557         559         567         538         486        1041\n",
      "         400         370         361         375         379         595         557         559         567         538        1065\n",
      "         402         400         370         361         375         607         595         557         559         567        1112\n",
      "         386         402         400         370         361         575         607         595         557         559        1118\n",
      "         398         386         402         400         370         568         575         607         595         557        1094\n",
      "         420         398         386         402         400         596         568         575         607         595        1088\n",
      "         412         420         398         386         402         613         596         568         575         607        1112\n",
      "         384         412         420         398         386         591         613         596         568         575        1095\n",
      "\n",
      "  Columns 12 through 22\n",
      "\n",
      "         873         893         895         869         592         571         555         535         502         913         867\n",
      "         884         873         893         895         617         592         571         555         535         946         913\n",
      "         942         884         873         893         601         617         592         571         555         909         946\n",
      "         947         942         884         873         586         601         617         592         571         914         909\n",
      "         937         947         942         884         576         586         601         617         592         949         914\n",
      "         946         937         947         942         575         576         586         601         617         964         949\n",
      "         994         946         937         947         556         575         576         586         601         915         964\n",
      "         989         994         946         937         552         556         575         576         586         914         915\n",
      "         970         989         994         946         574         552         556         575         576         971         914\n",
      "         997         970         989         994         596         574         552         556         575         984         971\n",
      "        1040         997         970         989         614         596         574         552         556         965         984\n",
      "        1062        1040         997         970         621         614         596         574         552         967         965\n",
      "        1041        1062        1040         997         645         621         614         596         574        1028         967\n",
      "        1065        1041        1062        1040         662         645         621         614         596        1046        1028\n",
      "        1112        1065        1041        1062         657         662         645         621         614        1013        1046\n",
      "        1118        1112        1065        1041         652         657         662         645         621        1019        1013\n",
      "        1094        1118        1112        1065         654         652         657         662         645        1058        1019\n",
      "        1088        1094        1118        1112         665         654         652         657         662        1062        1058\n",
      "        1112        1088        1094        1118         668         665         654         652         657        1016        1062\n",
      "\n",
      "  Columns 23 through 25\n",
      "\n",
      "         861         890         877\n",
      "         867         861         890\n",
      "         913         867         861\n",
      "         946         913         867\n",
      "         909         946         913\n",
      "         914         909         946\n",
      "         949         914         909\n",
      "         964         949         914\n",
      "         915         964         949\n",
      "         914         915         964\n",
      "         971         914         915\n",
      "         984         971         914\n",
      "         965         984         971\n",
      "         967         965         984\n",
      "        1028         967         965\n",
      "        1046        1028         967\n",
      "        1013        1046        1028\n",
      "        1019        1013        1046\n",
      "        1058        1019        1013\n",
      "\n",
      "\n",
      "A(:,:,2) =\n",
      "\n",
      "  Columns 1 through 11\n",
      "\n",
      "         388         371         371         399         412         506         488         498         521         502         884\n",
      "         386         388         371         371         399         515         506         488         498         521         942\n",
      "         360         386         388         371         371         476         515         506         488         498         947\n",
      "         365         360         386         388         371         463         476         515         506         488         937\n",
      "         381         365         360         386         388         482         463         476         515         506         946\n",
      "         376         381         365         360         386         499         482         463         476         515         994\n",
      "         350         376         381         365         360         479         499         482         463         476         989\n",
      "         354         350         376         381         365         486         479         499         482         463         970\n",
      "         379         354         350         376         381         538         486         479         499         482         997\n",
      "         375         379         354         350         376         567         538         486         479         499        1040\n",
      "         361         375         379         354         350         559         567         538         486         479        1062\n",
      "         370         361         375         379         354         557         559         567         538         486        1041\n",
      "         400         370         361         375         379         595         557         559         567         538        1065\n",
      "         402         400         370         361         375         607         595         557         559         567        1112\n",
      "         386         402         400         370         361         575         607         595         557         559        1118\n",
      "         398         386         402         400         370         568         575         607         595         557        1094\n",
      "         420         398         386         402         400         596         568         575         607         595        1088\n",
      "         412         420         398         386         402         613         596         568         575         607        1112\n",
      "         384         412         420         398         386         591         613         596         568         575        1095\n",
      "\n",
      "  Columns 12 through 22\n",
      "\n",
      "         873         893         895         869         592         571         555         535         502         913         867\n",
      "         884         873         893         895         617         592         571         555         535         946         913\n",
      "         942         884         873         893         601         617         592         571         555         909         946\n",
      "         947         942         884         873         586         601         617         592         571         914         909\n",
      "         937         947         942         884         576         586         601         617         592         949         914\n",
      "         946         937         947         942         575         576         586         601         617         964         949\n",
      "         994         946         937         947         556         575         576         586         601         915         964\n",
      "         989         994         946         937         552         556         575         576         586         914         915\n",
      "         970         989         994         946         574         552         556         575         576         971         914\n",
      "         997         970         989         994         596         574         552         556         575         984         971\n",
      "        1040         997         970         989         614         596         574         552         556         965         984\n",
      "        1062        1040         997         970         621         614         596         574         552         967         965\n",
      "        1041        1062        1040         997         645         621         614         596         574        1028         967\n",
      "        1065        1041        1062        1040         662         645         621         614         596        1046        1028\n",
      "        1112        1065        1041        1062         657         662         645         621         614        1013        1046\n",
      "        1118        1112        1065        1041         652         657         662         645         621        1019        1013\n",
      "        1094        1118        1112        1065         654         652         657         662         645        1058        1019\n",
      "        1088        1094        1118        1112         665         654         652         657         662        1062        1058\n",
      "        1112        1088        1094        1118         668         665         654         652         657        1016        1062\n",
      "\n",
      "  Columns 23 through 25\n",
      "\n",
      "         861         890         877\n",
      "         867         861         890\n",
      "         913         867         861\n",
      "         946         913         867\n",
      "         909         946         913\n",
      "         914         909         946\n",
      "         949         914         909\n",
      "         964         949         914\n",
      "         915         964         949\n",
      "         914         915         964\n",
      "         971         914         915\n",
      "         984         971         914\n",
      "         965         984         971\n",
      "         967         965         984\n",
      "        1028         967         965\n",
      "        1046        1028         967\n",
      "        1013        1046        1028\n",
      "        1019        1013        1046\n",
      "        1058        1019        1013\n",
      "\n",
      "\n",
      "A(:,:,3) =\n",
      "\n",
      "  Columns 1 through 11\n",
      "\n",
      "         388         371         371         399         412         506         488         498         521         502         884\n",
      "         386         388         371         371         399         515         506         488         498         521         942\n",
      "         360         386         388         371         371         476         515         506         488         498         947\n",
      "         365         360         386         388         371         463         476         515         506         488         937\n",
      "         381         365         360         386         388         482         463         476         515         506         946\n",
      "         376         381         365         360         386         499         482         463         476         515         994\n",
      "         350         376         381         365         360         479         499         482         463         476         989\n",
      "         354         350         376         381         365         486         479         499         482         463         970\n",
      "         379         354         350         376         381         538         486         479         499         482         997\n",
      "         375         379         354         350         376         567         538         486         479         499        1040\n",
      "         361         375         379         354         350         559         567         538         486         479        1062\n",
      "         370         361         375         379         354         557         559         567         538         486        1041\n",
      "         400         370         361         375         379         595         557         559         567         538        1065\n",
      "         402         400         370         361         375         607         595         557         559         567        1112\n",
      "         386         402         400         370         361         575         607         595         557         559        1118\n",
      "         398         386         402         400         370         568         575         607         595         557        1094\n",
      "         420         398         386         402         400         596         568         575         607         595        1088\n",
      "         412         420         398         386         402         613         596         568         575         607        1112\n",
      "         384         412         420         398         386         591         613         596         568         575        1095\n",
      "\n",
      "  Columns 12 through 22\n",
      "\n",
      "         873         893         895         869         592         571         555         535         502         913         867\n",
      "         884         873         893         895         617         592         571         555         535         946         913\n",
      "         942         884         873         893         601         617         592         571         555         909         946\n",
      "         947         942         884         873         586         601         617         592         571         914         909\n",
      "         937         947         942         884         576         586         601         617         592         949         914\n",
      "         946         937         947         942         575         576         586         601         617         964         949\n",
      "         994         946         937         947         556         575         576         586         601         915         964\n",
      "         989         994         946         937         552         556         575         576         586         914         915\n",
      "         970         989         994         946         574         552         556         575         576         971         914\n",
      "         997         970         989         994         596         574         552         556         575         984         971\n",
      "        1040         997         970         989         614         596         574         552         556         965         984\n",
      "        1062        1040         997         970         621         614         596         574         552         967         965\n",
      "        1041        1062        1040         997         645         621         614         596         574        1028         967\n",
      "        1065        1041        1062        1040         662         645         621         614         596        1046        1028\n",
      "        1112        1065        1041        1062         657         662         645         621         614        1013        1046\n",
      "        1118        1112        1065        1041         652         657         662         645         621        1019        1013\n",
      "        1094        1118        1112        1065         654         652         657         662         645        1058        1019\n",
      "        1088        1094        1118        1112         665         654         652         657         662        1062        1058\n",
      "        1112        1088        1094        1118         668         665         654         652         657        1016        1062\n",
      "\n",
      "  Columns 23 through 25\n",
      "\n",
      "         861         890         877\n",
      "         867         861         890\n",
      "         913         867         861\n",
      "         946         913         867\n",
      "         909         946         913\n",
      "         914         909         946\n",
      "         949         914         909\n",
      "         964         949         914\n",
      "         915         964         949\n",
      "         914         915         964\n",
      "         971         914         915\n",
      "         984         971         914\n",
      "         965         984         971\n",
      "         967         965         984\n",
      "        1028         967         965\n",
      "        1046        1028         967\n",
      "        1013        1046        1028\n",
      "        1019        1013        1046\n",
      "        1058        1019        1013\n",
      "\n",
      "\n",
      "A(:,:,4) =\n",
      "\n",
      "  Columns 1 through 11\n",
      "\n",
      "         388         371         371         399         412         506         488         498         521         502         884\n",
      "         386         388         371         371         399         515         506         488         498         521         942\n",
      "         360         386         388         371         371         476         515         506         488         498         947\n",
      "         365         360         386         388         371         463         476         515         506         488         937\n",
      "         381         365         360         386         388         482         463         476         515         506         946\n",
      "         376         381         365         360         386         499         482         463         476         515         994\n",
      "         350         376         381         365         360         479         499         482         463         476         989\n",
      "         354         350         376         381         365         486         479         499         482         463         970\n",
      "         379         354         350         376         381         538         486         479         499         482         997\n",
      "         375         379         354         350         376         567         538         486         479         499        1040\n",
      "         361         375         379         354         350         559         567         538         486         479        1062\n",
      "         370         361         375         379         354         557         559         567         538         486        1041\n",
      "         400         370         361         375         379         595         557         559         567         538        1065\n",
      "         402         400         370         361         375         607         595         557         559         567        1112\n",
      "         386         402         400         370         361         575         607         595         557         559        1118\n",
      "         398         386         402         400         370         568         575         607         595         557        1094\n",
      "         420         398         386         402         400         596         568         575         607         595        1088\n",
      "         412         420         398         386         402         613         596         568         575         607        1112\n",
      "         384         412         420         398         386         591         613         596         568         575        1095\n",
      "\n",
      "  Columns 12 through 22\n",
      "\n",
      "         873         893         895         869         592         571         555         535         502         913         867\n",
      "         884         873         893         895         617         592         571         555         535         946         913\n",
      "         942         884         873         893         601         617         592         571         555         909         946\n",
      "         947         942         884         873         586         601         617         592         571         914         909\n",
      "         937         947         942         884         576         586         601         617         592         949         914\n",
      "         946         937         947         942         575         576         586         601         617         964         949\n",
      "         994         946         937         947         556         575         576         586         601         915         964\n",
      "         989         994         946         937         552         556         575         576         586         914         915\n",
      "         970         989         994         946         574         552         556         575         576         971         914\n",
      "         997         970         989         994         596         574         552         556         575         984         971\n",
      "        1040         997         970         989         614         596         574         552         556         965         984\n",
      "        1062        1040         997         970         621         614         596         574         552         967         965\n",
      "        1041        1062        1040         997         645         621         614         596         574        1028         967\n",
      "        1065        1041        1062        1040         662         645         621         614         596        1046        1028\n",
      "        1112        1065        1041        1062         657         662         645         621         614        1013        1046\n",
      "        1118        1112        1065        1041         652         657         662         645         621        1019        1013\n",
      "        1094        1118        1112        1065         654         652         657         662         645        1058        1019\n",
      "        1088        1094        1118        1112         665         654         652         657         662        1062        1058\n",
      "        1112        1088        1094        1118         668         665         654         652         657        1016        1062\n",
      "\n",
      "  Columns 23 through 25\n",
      "\n",
      "         861         890         877\n",
      "         867         861         890\n",
      "         913         867         861\n",
      "         946         913         867\n",
      "         909         946         913\n",
      "         914         909         946\n",
      "         949         914         909\n",
      "         964         949         914\n",
      "         915         964         949\n",
      "         914         915         964\n",
      "         971         914         915\n",
      "         984         971         914\n",
      "         965         984         971\n",
      "         967         965         984\n",
      "        1028         967         965\n",
      "        1046        1028         967\n",
      "        1013        1046        1028\n",
      "        1019        1013        1046\n",
      "        1058        1019        1013\n",
      "\n",
      "\n",
      "A(:,:,5) =\n",
      "\n",
      "  Columns 1 through 11\n",
      "\n",
      "         388         371         371         399         412         506         488         498         521         502         884\n",
      "         386         388         371         371         399         515         506         488         498         521         942\n",
      "         360         386         388         371         371         476         515         506         488         498         947\n",
      "         365         360         386         388         371         463         476         515         506         488         937\n",
      "         381         365         360         386         388         482         463         476         515         506         946\n",
      "         376         381         365         360         386         499         482         463         476         515         994\n",
      "         350         376         381         365         360         479         499         482         463         476         989\n",
      "         354         350         376         381         365         486         479         499         482         463         970\n",
      "         379         354         350         376         381         538         486         479         499         482         997\n",
      "         375         379         354         350         376         567         538         486         479         499        1040\n",
      "         361         375         379         354         350         559         567         538         486         479        1062\n",
      "         370         361         375         379         354         557         559         567         538         486        1041\n",
      "         400         370         361         375         379         595         557         559         567         538        1065\n",
      "         402         400         370         361         375         607         595         557         559         567        1112\n",
      "         386         402         400         370         361         575         607         595         557         559        1118\n",
      "         398         386         402         400         370         568         575         607         595         557        1094\n",
      "         420         398         386         402         400         596         568         575         607         595        1088\n",
      "         412         420         398         386         402         613         596         568         575         607        1112\n",
      "         384         412         420         398         386         591         613         596         568         575        1095\n",
      "\n",
      "  Columns 12 through 22\n",
      "\n",
      "         873         893         895         869         592         571         555         535         502         913         867\n",
      "         884         873         893         895         617         592         571         555         535         946         913\n",
      "         942         884         873         893         601         617         592         571         555         909         946\n",
      "         947         942         884         873         586         601         617         592         571         914         909\n",
      "         937         947         942         884         576         586         601         617         592         949         914\n",
      "         946         937         947         942         575         576         586         601         617         964         949\n",
      "         994         946         937         947         556         575         576         586         601         915         964\n",
      "         989         994         946         937         552         556         575         576         586         914         915\n",
      "         970         989         994         946         574         552         556         575         576         971         914\n",
      "         997         970         989         994         596         574         552         556         575         984         971\n",
      "        1040         997         970         989         614         596         574         552         556         965         984\n",
      "        1062        1040         997         970         621         614         596         574         552         967         965\n",
      "        1041        1062        1040         997         645         621         614         596         574        1028         967\n",
      "        1065        1041        1062        1040         662         645         621         614         596        1046        1028\n",
      "        1112        1065        1041        1062         657         662         645         621         614        1013        1046\n",
      "        1118        1112        1065        1041         652         657         662         645         621        1019        1013\n",
      "        1094        1118        1112        1065         654         652         657         662         645        1058        1019\n",
      "        1088        1094        1118        1112         665         654         652         657         662        1062        1058\n",
      "        1112        1088        1094        1118         668         665         654         652         657        1016        1062\n",
      "\n",
      "  Columns 23 through 25\n",
      "\n",
      "         861         890         877\n",
      "         867         861         890\n",
      "         913         867         861\n",
      "         946         913         867\n",
      "         909         946         913\n",
      "         914         909         946\n",
      "         949         914         909\n",
      "         964         949         914\n",
      "         915         964         949\n",
      "         914         915         964\n",
      "         971         914         915\n",
      "         984         971         914\n",
      "         965         984         971\n",
      "         967         965         984\n",
      "        1028         967         965\n",
      "        1046        1028         967\n",
      "        1013        1046        1028\n",
      "        1019        1013        1046\n",
      "        1058        1019        1013\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "D_tau = 5; % the number of steps to look back for past data\n",
    "weight = zeros(NumOfItems,NumOfItems,D_tau);\n",
    "A = []; % For each item, i.e. A(:,:,1) & A(:,:,2), ... matrices are same!!!\n",
    "ww = zeros(D_tau*NumOfItems,1);\n",
    "\n",
    "\n",
    "for it = 1:NumOfItems\n",
    "    for m = D_tau+1:NumOfMonths\n",
    "      pos = 1;\n",
    "      for j = 1:NumOfItems\n",
    "        for i = 1:D_tau\n",
    "              A(m-D_tau,pos,it) =  salesdata(floor((pos-1)/D_tau)+1,m-i);\n",
    "              pos = pos + 1;\n",
    "        end\n",
    "      end\n",
    "    end\n",
    "    \n",
    "    ww = A(:,:,it)\\salesdata(it,D_tau+1:NumOfMonths)';\n",
    "    for j = 1:NumOfItems\n",
    "        weight(it,j,:) = ww(D_tau*(j-1)+1:D_tau*j);\n",
    "    end\n",
    "end\n",
    "A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "predictedSales =\n",
      "\n",
      "   1.0e+03 *\n",
      "\n",
      "    0.4476\n",
      "    0.6923\n",
      "    1.2330\n",
      "    0.7708\n",
      "    1.2086\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "%% prediction for next month only\n",
    "NumOfPredictedMonths = 1;\n",
    "predictedSales = zeros(NumOfItems,NumOfPredictedMonths);   % for next month only\n",
    "predA = [];\n",
    "tempMatrix = zeros(NumOfItems,D_tau);\n",
    "for it=1:NumOfItems\n",
    "    for m = NumOfMonths+1:NumOfMonths+NumOfPredictedMonths\n",
    "        for pos = 1:D_tau*NumOfItems\n",
    "            predA(it,pos) = salesdata(floor((pos-1)/D_tau)+1,m-D_tau+mod(pos+1,D_tau));\n",
    "        end\n",
    "    end\n",
    "    tempMatrix0 = weight(it,:,:);\n",
    "  \n",
    "    for tt = 1:size(tempMatrix0,2)\n",
    "        tempMatrix1 = tempMatrix0(1,tt,:);\n",
    "        for tau = 1:size(tempMatrix1,3)\n",
    "            tempMatrix(tt,tau) = tempMatrix1(:,:,tau);\n",
    "        end\n",
    "    end\n",
    "    %tempMatrix = tempMatrix';\n",
    "        \n",
    "    predictedSales(it,1) = predA(it,:)*reshape(tempMatrix',D_tau*NumOfItems,1);\n",
    "end\n",
    "\n",
    "predictedSales\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "image/png": 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VN0kmQAAkQAL6AyJg9FqWxfb/BlylKFwd4NCx0QiJEEIAAHJIe8SaAB7oBPCA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\n+rmHMJUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<IPython.core.display.Image object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%% plot of sales data + predictedsalesdata\n",
    "t = (1:NumOfMonths)';       % months\n",
    "\n",
    "subplot(122)\n",
    "colQR = {'bs','gs','rs','cs','ms'};\n",
    "\n",
    "hold on\n",
    "for i = 1:NumOfItems\n",
    "    plot(t,salesdata(i,:),col{i});\n",
    "end\n",
    "\n",
    "hleg = legend('Item 1','Item 2','Item 3','Item 4','Item 5');\n",
    "set(hleg,'Location','northwest');\n",
    "xlabel('Month'), ylabel('Number of Items Sold'), title('Sales data + Prediction')\n",
    "\n",
    "for i = 1:NumOfItems\n",
    "        plot((NumOfMonths+1:NumOfMonths+NumOfPredictedMonths),predictedSales(i,1),colQR{i})\n",
    "end"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Errors (Euclidean norm)\n",
      "\n",
      "error =\n",
      "\n",
      "   1.0e+03 *\n",
      "\n",
      "    0.1275\n",
      "    0.2540\n",
      "    0.3454\n",
      "    0.2652\n",
      "    0.4396\n",
      "    1.4317\n",
      "\n",
      "\n"
     ]
    }
   ],
   "source": [
    "error = zeros(NumOfItems+1,1);      % last row is sum\n",
    "for i=1:NumOfItems\n",
    "    error(i,1) = norm(salestestdata(i,:)-predictedSales(i,1));\n",
    "end\n",
    "error(NumOfItems+1,:) = sum(error(1:NumOfItems,:),1);\n",
    "disp('Errors (Euclidean norm)')\n",
    "error     "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Matlab",
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